SSTQ:Privacy-Preserving Vector Quantization via Subsampled Stochastic TurboQuant

Abstract:Achieving local differential privacy in distributed optimization while maintaining low communication cost remains challenging. Existing vector quantization methods, such as vqSGD, use high-dimensional geometric constructions but incur unfavorable dimension-dependent variance. In this work, we propose Subsampled Stochastic TurboQuant (SSTQ), a framework that combines overcomplete equal-norm tight frames, coordinate subsampling, and privacy-aware one-dimensional quantization. SSTQ includes two variants: a Flat Randomized Response version and a Metric-Aware Laplace version, the latter being better suited to higher codebook bit-width regimes. We show that SSTQ achieves optimal mean squared error scaling while using only $\lceil \log_2 N \rceil + b$ bits per client, where $N = \Theta(d)$ is the frame size. We also derive a surrogate privacy-aware codebook objective that reduces the codebook-dependent MSE scaling from $O(4^b)$ to $O(2^b)$. Finally, we empirically evaluate SSTQ against established baselines on federated learning tasks using CIFAR-10 and Fashion-MNIST, demonstrating favorable utility and communication efficiency.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)

arXiv:2608.05127 [cs.LG]

(or arXiv:2608.05127v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.05127 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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